Solve for $x$ and $y$ using elimination. ${-3x-2y = -21}$ ${3x+5y = 30}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $3y = 9$ $\dfrac{3y}{{3}} = \dfrac{9}{{3}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-3x-2y = -21}\thinspace$ to find $x$ ${-3x - 2}{(3)}{= -21}$ $-3x-6 = -21$ $-3x-6{+6} = -21{+6}$ $-3x = -15$ $\dfrac{-3x}{{-3}} = \dfrac{-15}{{-3}}$ ${x = 5}$ You can also plug ${y = 3}$ into $\thinspace {3x+5y = 30}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(3)}{= 30}$ ${x = 5}$